Geometry of second adjointness for p-adic groups

We present a geometric proof of Bernstein's second adjointness for a reductive $p$-adic group. Our approach is based on geometry of the wonderful compactification and related varieties. Considering asymptotic behavior of a function on the group in a neighborhood of a boundary stratum of the compactification, we get a "co-specialization" map between spaces of functions on various varieties with $G\times G$ action. These maps can be viewed as maps of bimodules for the Hecke algebra, and the corresponding natural transformations of functors lead to the second adjointness. We also get a formula for the "co-specialization" map expressing it as a composition of the orishperic transform and inverse intertwining operator; a parallel result for $D$-modules was obtained in arXiv:0902.1493. As a byproduct we obtain a formula for the Plancherel functional restricted to a certain commutative subalgebra in the Hecke algebra, generalizing a result by Opdam.Comment: 40 pages; minor, mostly typographical corrections; final versio

A categorical approach to the stable center conjecture

The stable center conjecture asserts that the space of stable distributions in the Bernstein center of a reductive p-adic is closed under convolution. It is closely related to the notion of an L-packet and endoscopy theory. We describe a categorical approach to the depth zero part of the conjecture. As an illustration of our method, we show that the Bernstein projector to the depth zero spectrum is stable.Comment: 74 pages, a grant acknowledgement is change

On the depth r Bernstein projector

In this paper we prove an explicit formula for the Bernstein projector to representations of depth at most r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth r Bernstein projector is stable. Moreover, for integral depths our proof is purely local.Comment: 42 pages, a grant acknowledgement is change

Geographic trends in range sizes explain patterns in bird responses to urbanization in Europe

The probability of occurrence of bird species in towns/cities increases with their range sizes, and Rapoport’s rule states that range sizes increase with latitude. To test the hypothesis that the increasing number of bird species persisting in cities at higher latitudes of Europe is linked to their larger range sizes, we compiled data on bird communities of: a) 41 urban bird atlases; b) 37 city core zones from published sources; c) regions of nine grid cells of the EBCC Atlas of European Breeding Birds around each city. We tested whether the proportion of species from particular regional bird assemblages entering cities (i.e., proportional richness) was related to the geographical  position, mean range size of regional avifaunas, proportion of vegetated areas and city habitat heterogeneity. The mean range sizes of the observed and randomly selected urban avifaunas were contrasted. The proportional richness of urban avifaunas was positively related to the geographic position and mean range size of birds in regional assemblages. The evidence favoured range sizes if considering the European range sizes or latitudinal extents, but was limited for global range sizes. Randomizations tended to show larger range sizes for the real avifaunas than in the randomly selected ones. For urban core zones, the results were less clear-cut with some evidence only in favour of the European range sizes. No role of vegetation or habitat heterogeneity was found. In conclusion, while vegetation availability or heterogeneity did not show any effects, spatial position and range sizes of birds in regional assemblages seemed to influence the proportional richness of cities and their core zones. Factors correlated with spatial position (e.g., climate) might increase the attractivity of particular cities to birds. However, the effects of range sizes indicated that urbanization possibly has more negative impacts on the avifauna in the regions occupied by less widespread species

Horizon Feedback Inflation

We consider the effect of the Gibbons-Hawking radiation on the inflaton in the situation where it is coupled to a large number of spectator fields. We argue that this will lead to two important effects - a thermal contribution to the potential and a gradual change in parameters in the Lagrangian which results from thermodynamic and energy conservation arguments. We present a scenario of hilltop inflation where the field starts trapped at the origin before slowly experiencing a phase transition during which the field extremely slowly moves towards its zero temperature expectation value. We show that it is possible to obtain enough e-folds of expansion as well as the correct spectrum of perturbations without hugely fine-tuned parameters in the potential (albeit with many spectator fields). We also comment on how initial conditions for inflation can arise naturally in this situation.Comment: v1: 17 pages, 5 figures. v2: updated discussion and references, removed typos, submitted to journal. v3: minor revisions, version published in EPJ

EVALUATING THE IMPACTS OF AGRICULTURAL EXPORTS ON A REGIONAL ECONOMY

Agricultural exports are important to many regional economies, as is the case for agricultural exports wither produced in or shipped through Louisiana. A hybrid (revised and verified) IMPLAN model of the Louisiana economy is used to estimate the direct and indirect impact of agricultural exports. Original model estimates of foreign exports lacked holistic (overall) accuracy. However, other, more general uses of the model were unaffected by this lack of accuracy. While the contributions of agricultural exports to the state economy were substantial, impacts were concentrated in unprocessed products. Increasing the export of processed agricultural products should enhance economic activity.Agricultural exports, Holistic accuracy, IMPLAN, Input-output models, Processed exports, Community/Rural/Urban Development, International Relations/Trade,